Question

Use division algorithm to show that any positive odd integer is of the form 6q+1, or 6q+3 or 69 +5, where q is some integer.​

Answer 1

Hey there,

step by step ->

by (Divison algorithm)

Let a be any positive integer and b=6.

Then by division algorithm,

a=6q+r where r=0,1,2,3,4,5

So, a is of the form 6q,6q+1,6q+2,6q+3,6q+3,6q+4,6q+5.

Therefore if a is an odd integer then a is of the form 6q+1 or 6q+3 6q+5.

Hence proved.

HOPE THIS HELPS

THANKS

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